Demcracies at war with each other (off the top of my head):
The United States of America vs the Confederate States of America
Allies vs Finland - Finland was allied with Germany against the Soviet Union at the time.
United States of America vs Vietnam - There was suppose to be an election to decide the government of Vietnam, but Ho Chi Min had support of 90% of the population so instead of allowing an election America installed a South Korea puppet state.
Israel vs Lebanon
Israel vs Palestine - Not exactly a war between two countries, but the Palestinians did elect Yasser Arafat and later Hamas into power, both of which supported fighting Israel using guerilla tactics and terrorism.
Russia vs Georgia - If you call that a war, but it would have been if Georgia wasnt so weak that they were unable to defend themselves.
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The term democracy is vague. I would define how democratic country is by how many people can participate in government. In modern America, about 75% of the population, or all adults over the age of 18 who are not felons can vote, but 200 years ago only white males could vote, measuring about 20% of the population. In the Soviet Union, only members of the communist party could vote, consisting of about 10% of the population. What is a democracy and what is not? You could make arguments anyway, but obviously some are more or less democratic than others.
Democracies can and do declare wars on each other, is just far less likely because modern democracies tend to be highly similar socially and heavily integrated economically. For instance, the United States and Canada are so intertwinned that a war would never make sense as continued cooperation with a very friendly country is much more beneficial than war. On the otherhand, Israel and Lebanon have fought two wars because they do not have much in common economically or socially, though social (religion) would be the major factor here.
